Quick question, does the burn damage from the fire godlikes passive improve with gear like ring or focused flame or stuff that increases fire abilities power levels?

It does, bit it doesn't properly scale with level in the unmodified game iirc - so it becomes a bit moot after some levels. 

even at low level it's pretty moot. the fire godlike buff should mostly be seen as a conditional AR boost

Ah well, thanks for the replies